Properties of Exercise Strategies

TL;DR

This paper presents a formal framework for providing precise, semantically rich feedback in mathematical learning environments, ensuring correctness through formal specifications and proofs across various mathematical domains.

Contribution

It introduces a formal description of feedback concepts and verifies their properties to enhance reliability in educational feedback services.

Findings

Feedback services are correct for logic, algebra, and linear algebra exercises.

Formal specifications enable reasoning about feedback correctness.

Explicit property requirements improve confidence in feedback accuracy.

Abstract

Mathematical learning environments give domain-specific and immediate feedback to students solving a mathematical exercise. Based on a language for specifying strategies, we have developed a feedback framework that automatically calculates semantically rich feedback. We offer this feedback functionality to mathematical learning environments via a set of web services. Feedback is only effective when it is precise and to the point. The tests we have performed give some confidence about the correctness of our feedback services. To increase confidence in our services, we explicitly specify the properties our feedback services should satisfy, and, if possible, prove them correct. For this, we give a formal description of the concepts used in our feedback framework services. The formalisation allows us to reason about these concepts, and to state a number of desired properties of the concepts. Our feedback services use exercise descriptions for their instances on domains such as logic, algebra, and linear algebra. We formulate requirements these domain descriptions should satisfy for the feedback services to react as expected.